I will present a construction of a scattered compact topological space that answered a question due to Wiesław Kubiś and Arkady Leiderman. The construction is contained in a joint paper with Petr Hájek, Jacopo Somaglia, and Stevo Todorčević. The purpose of the paper was actually to answer a problem in Banach space theory, but for the sake of the talk I will focus on the construction of the compact space and not mention Banach spaces at all. In the talk I will give a short introduction to Descriptive Topology in order to explain the setting and to motivate the construction of the example. Then I will explain how to use the combinatorics of the set of countable ordinals, in particular Todorčević's theory of walks on ordinals, for the construction of the example.

P.Hájek, T.Russo, J.Somaglia, and S.Todorčević,

An Asplund space with norming Markuševič basis that is not weakly compactly generated,

https://doi.org/10.1016/j.aim.2021.108041

Adv. Math. 392 (2021... more

P.Hájek, T.Russo, J.Somaglia, and S.Todorčević,

An Asplund space with norming Markuševič basis that is not weakly compactly generated,

https://doi.org/10.1016/j.aim.2021.108041

Adv. Math. 392 (2021... more